The 5-meter-long (16-foot-long), 40-kilogram (90-pound) iron sign at the Holocaust memorial site in southern Poland was unscrewed on one side and torn off on the other, police spokeswoman Katarzyna Padlo said.
The theft from the entrance to the camp - where more than 1 million people, mostly Jews, died during World War II - brought condemnation worldwide.
"The theft of such a symbolic object is an attack on the memory of the Holocaust, and an escalation from those elements that would like to return us to darker days," Yad Vashem Chairman Avner Shalev said in a statement from Jerusalem.
"I call on all enlightened forces in the world who fight against anti-Semitism, racism, xenophobia and the hatred of the other, to join together to combat these trends."
The sign disappeared from the Auschwitz memorial between 3:30 a.m. and 5 a.m., Padlo said.
Police deployed 50 police, including 20 detectives, and a search dog to the Auschwitz grounds, where barracks, watchtowers and ruins of gas chambers stand as testament to the atrocities of Nazi Germany.
Police said they were reviewing footage from a surveillance camera that overlooks the entrance gate and the road beyond, but declined to say whether the crime was recorded.
Auschwitz museum spokesman Jaroslaw Mensfelt said it might have been too dark for the camera to have captured images.
He said the thieves apparently carried the sign 300 meters (yards) to an opening in a concrete wall. That opening had been left intentionally to preserve a poplar tree dating back to the time of the war.
Four metal bars that had blocked the opening were cut. Tire tracks and footprints in the snow led from the wall opening to the nearby road, where police presume the sign was loaded on to a vehicle.
Poland's chief rabbi, Michael Schudrich, said he had trouble imagining who would steal the sign.
"If they are pranksters, they'd have to be sick pranksters, or someone with a political agenda. But whoever has done it has desecrated world memory," Schudrich said.
He said the theft could have been committed by neo-Nazi extremists, or even people scheming to sell the sign of the black market.
"There's a market for everything," he said, adding that it was "like stealing a Picasso. Even a hot Picasso you could try to move after 10 years - but not this."
An exact replica of the sign, produced when the original received restoration work years ago, was quickly hung in its place.
In Brussels, European Parliament president Jerzy Buzek, a former Polish prime minister, appealed to the thieves to return the sign.
"Give it back out of respect for the suffering of over a million victims, murdered in this Nazi camp, the biggest cemetery of humankind," Buzek said.
Polish President Lech Kaczynski said he was "shaken and outraged" by the theft of a "world-known symbol of Nazi cynicism and cruelty." He appealed to all Poles for help finding it.
Police were offering a 5,000-zloty ($1,700) reward for public tipoffs about the thieves.
In Jerusalem, the International Auschwitz Committee said the theft "deeply unsettles the survivors."
"The sign has to be found," said Noach Flug, an Auschwitz survivor and president of the committee. "The slogan and the camp itself will tell what happened even when we won't be able to tell anymore."
After occupying Poland in 1939, the Nazis established the Auschwitz I camp in the southern Polish city of Oswiecim and initially used it for German political prisoners and non-Jewish Polish prisoners, who began arriving in June 1940.
Nazi guards ordered Polish inmates to make the original sign shortly thereafter in the camp's iron workshop, museum spokesman Pawel Sawicki said.
Two years later, hundreds of thousands of Jews began arriving by cattle trains to the wooden barracks of nearby Birkenau, also called Auschwitz II, where most were killed in gas chambers.
The slogan "Arbeit Macht Frei" appeared at the entrances of other Nazi camps, including Dachau and Sachsenhausen. The long curving sign at Auschwitz is considered the best known.
Today the Auschwitz site attracts more than 1 million visitors annually.
This week Germany pledged euro60 million ($87 million) - half the estimated amount required - to a new endowment that will fund long-term preservation work.
This was the first major act of vandalism at the site, which previously has suffered graffiti including spray-painted swastikas.
Other Holocaust memorials have suffered neo-Nazi vandalism. Sachsenhausen on the outskirts of Berlin was attacked in 1992, when two barracks were set on fire. That crime remains unsolved.
Scislowska reported from Warsaw. Associated Press Writers Vanessa Gera in Warsaw, David Rising and Kirsten Grieshaber in Berlin, Raf Casert in Brussels, and Aron Heller in Jerusalem contributed to this report.